A035126
Squares when digits rotated right once remain square.
Original entry on oeis.org
1, 4, 9, 256, 441, 961, 16641, 48841, 61009, 66564, 1127844, 2537649, 3857296, 4932841, 182682256, 298840369, 342842256, 392872041, 493772841, 787588096, 877996161, 10766967696, 33255899044, 49382172841, 74825772849
Offset: 1
2221^2 = 4932841 -> 1493284 = 1222^2. Note that the root behaves accordingly!
-
[k:k in [m^2:m in [1..10^6]]| IsSquare(Seqint( (Intseq(Floor(k/10)) cat [ Intseq(k)[1]])))]; // Marius A. Burtea, Oct 08 2019
-
Select[Range[300000]^2,IntegerQ[Sqrt[FromDigits[RotateRight[ IntegerDigits[ #]]]]]&] (* Harvey P. Dale, Mar 22 2015 *)
-
from itertools import count, islice
from sympy.solvers.diophantine.diophantine import diop_DN
def A035126_gen(): # generator of terms
for l in count(0):
l1, l2 = 10**(l+1), 10**l
yield from sorted(set(x**2 for z in (diop_DN(10,m*(1-l1)) for m in range(10)) for x, y in z if l1 >= x**2 >= l2))
A035126_list = list(islice(A035126_gen(),30)) # Chai Wah Wu, Apr 23 2022
A035128
Rotating digits of a(n)^3 right once still yields a cube.
Original entry on oeis.org
379^3 = 54439939 -> 95443993 = 457^3.
-
[k:k in [1..100000]| IsPower(Seqint((Intseq(Floor(k^3/10)) cat [Intseq(k^3)[1]])),3)]; // Marius A. Burtea, Oct 08 2019
-
Select[Range[500], IntegerQ @ Surd[FromDigits @ RotateRight @ IntegerDigits[#^3], 3] &] (* Amiram Eldar, Oct 08 2019 *)
A035131
Cubes that when digits rotated left once remain cubic.
Original entry on oeis.org
1, 8, 512, 95443993
Offset: 1
-
Select[Range[500]^3, (d = RotateLeft @ IntegerDigits[#])[[1]] > 0 && IntegerQ @ Surd[FromDigits @ d, 3] &] (* Amiram Eldar, Oct 08 2019 *)
A353054
Numbers k such that placing the last digit first gives 2k+1.
Original entry on oeis.org
1052, 26315, 15789473, 3157894736, 421052631578, 2105263157894, 36842105263157, 1052631578947368421052, 26315789473684210526315, 15789473684210526315789473, 3157894736842105263157894736, 421052631578947368421052631578, 2105263157894736842105263157894, 36842105263157894736842105263157
Offset: 1
2*1052 + 1 = 2105. Thus, 1052 is in this sequence.
-
Select[Range[100000000], FromDigits[Prepend[Drop[IntegerDigits[#], -1], Last[IntegerDigits[#]]]] == 2 # + 1 &]
-
f(n) = if (n < 10, n, my(d=digits(n)); fromdigits(concat(d[#d], Vec(d, #d-1))));
isok(m) = f(m) == 2*m+1; \\ Michel Marcus, Apr 21 2022
-
from itertools import count, islice
def A353054_gen(): # generator of terms
for l in count(1):
a, b = 10**l-2, 10**(l-1)-2
for m in range(1,10):
q, r = divmod(m*a-1,19)
if r == 0 and b <= q - 2 <= a:
yield 10*q+m
A353054_list = list(islice(A353054_gen(),20)) # Chai Wah Wu, Apr 23 2022
Showing 1-4 of 4 results.
Comments